JPH0715707B2 - High resolution image compression method and apparatus - Google Patents

Description

Description: TECHNICAL FIELD The present invention relates to high resolution image compression techniques, and more particularly, to a larger compressed high resolution icon image representing the operational state of the integrated circuit under test. A method and apparatus for dynamic imaging of motion defects in an integrated circuit formed from an image.

2. Description of the Related Art As the internal feature size of very large scale (VLSI) integrated circuits decreases, the demand for faster and more reliable design and testing is increasing. Conventional integrated circuit (IC) testers are only capable of retrieving information from the external pins of the device under test (DUT), thus limiting subsequent diagnostics. Defects detected by conventional testers may be caused by misalignment at any point inside the component. If the DUT has thousands of gates, identifying defects becomes a very complex and difficult problem.

In a typical test operation, a conventional IC tester (providing excitation to an input pin of an IC and measuring the result at an IC output pin) will test for any vector (in a test vector sequence) when testing an IC device. For example,
The defect in the vector v) is detected. This test sequence may have a large number of test vectors, for example 100 or more, and a set such as the input voltage applied to the pins of the DUT for each vector. Represents the excitation of. The source of the detected defect is somewhere in the chip, and any vector between the first vector in the sequence (vector 1) and the vector in which the defect was detected (vector v) (eg vector a). ) Occurs in. Thus, this defect propagates forward and appears at the vector v at the external pin or bond pad of the DUT. Therefore, it is desirable to identify, or identify, the nature, location, and time of occurrence of defects in vector a.

Therefore, it is necessary to perform an internal probe of the chip.
For many years, the preferred solution has been to probe the chip using a low energy (about 1 keV) scanning electron microscope (SEM). For example, E. Menzel and E. Kubalek, "Basics of Electron Beam Testing of Integrated Circuits (Fundamenta
ls of Electron Beam Testing of Integarated
Circuits), 5 Scanning 103-122 (1983), and E. Plies and G. Otto, "Voltage Mea inside Integrated Circuits Using Mechanical and Electronic Probes."
surement Inside Integrated Circuit Using Mech
anical and Electron Probes) ”, IV Scanning Electron Microscopy 1491-1500 (1985).

Until recently, SEMs were sophisticated laboratory equipment and were used only by skilled researchers. In 1987, an electron beam test system based on the "IDS 5000" workstation was marketed by Schlumberger. S. Concina, G. Liu, L. Lattanzi,
S. Reyfman, N. Richardson, “Software Integration in a Workstation-based Electron Beam Tester
Based E-Beam Tester) ", International
Test Conference Proceedings (1986),
N. Richardson, "E-Beam Probing for VLSI Circuit Debu
g) ”, VLSI Systems Design (1987), S. Concin
N. Richardson, “IDS 5000: an Integrated Diagnosis System for VLSI (IDS 5000: an Integrated Diagnosis System
For VLSI) ”, 7 Microelectronic Engineering (1987) and the like. Further, U.S. Pat. No. 4,70, issued to N. Richardson
See 6,019 and 4,721,909.

Therefore, measurement and information gathering is not a major issue when analyzing IC defects. However, organizing the extensive and detailed information obtained about ICs in such testers is important for making rapid and effective defect diagnosis.

Rather than seeking an answer to an absolute problem ("Why does this device malfunction?"), It is desirable to treat it as a relative problem ("This device behaves differently than known good devices). Where, when, and why? ”). According to this latter diagnostic method,
It is possible to trace operational defects in the IC.

To make such a diagnosis, select the time period of interest between 0 (the start of the test sequence of interest) and the first defect detection. This period is divided into a plurality of intervals so that the IC performs a constant operation at each interval. Therefore, each interval corresponds to the operating state of the IC. After the states of interest have been identified, a comparison can be made between the known "good" IC device and the DUT in each state.

Such a comparison can be made with a strobe voltage contrast image. The device under test (DUT) is excited with a series of test "vectors" in a conventional electron beam test system, such as the Schlumberger "IDS 5000". Each test "vector" is, for example,
It represents a specific set of excitations, such as the input voltage applied to an IC pin. During the application of each vector in the sequence, the DUT is in a state for a time period called "strobe window". By repeatedly pulsing the electron beam in a phase relative to the start of the sequence, the DU in any desired strobe window is
It is possible to obtain a strobe image representing the state of T. This strobe process is similar to using strobe lights to "freeze" the operation of an automobile engine to adjust ignition timing. A series of state images form a stack.

This process is repeated using a known good IC device (also called a golden die) to obtain a stack of strobe images representing the condition in response to the same set of test vectors. For example, each image has 0 intensity.
, And a graphical representation in digital form in the form of a 512 × 512 matrix of pixels of variable intensity represented by a value between 8 and 255 (8-bit value). The images so obtained represent the operating conditions of the DUT and can be stored and used to diagnose operational defects in the DUT.

After obtaining the images, it is possible to compare the stacks. This comparison can take the form of subtracting the golden die image from the DUT image on a pixel-by-pixel basis, in which case the compared images are generated in response to the same set of excitations. is there. This comparison is repeated for each image to produce a stack of "difference" images.

On the other hand, these two stacks can represent the states of a single DUT in response to two different sets of excitations. For example, the DUT may operate as designed at a given temperature or for a given input voltage, but may fail at higher temperatures or input voltages. It is possible to obtain an image of the stack that represents the correct operation of the DUT under one set of conditions and a second stack that represents a malfunction under the second set of conditions. It is also possible to compare these stacks image by image to generate a stack of "difference" images.

If a good device and a defective device operate in the same correspondence, their images are the same. Similarly, if a device to which different sets of excitations are applied operates in the same correspondence in response to the different sets of excitations, their images will be the same. Deviations between these two sets of images can be considered to be deviations in the test (ie defective) equipment. T. May, G. Scott, E. Meieran, P. W.
iener, V. Rao, “Dynamic Fault Imaging of VLSI Ran
dom Logic Devices ”, International Physics Symposium Proceedings (1984). Based on one image per state, this comparison process represents the propagation of a defect from its origin to where it was first detected.
This defect may appear as a shift in the difference image, for example a black or white line in an otherwise gray difference image could represent an incorrect logic level in the DUT. Such a comparison process is known as "Dynamic Fault Imaging" (DFI).

Of course, if this comparison works correctly, the stacks of these two images must represent the same conditions, i.e. the same chips of the same magnification imaged under the same SEM operating conditions. Represents an area. However, the images in one stack may be skewed or rotated with respect to the images in another stack because the tip orientation was slightly different with respect to the SEM when the images were acquired. Since a perfect alignment is not possible, it is necessary to perform a "spatial warping" operation on each image in one stack in order to align each image with the corresponding image in the other stack. There are cases.

Once the images have been acquired, filtered, matched and pixel-by-pixel compared to form the resulting "difference" image stack, these difference images are displayed to propagate defect propagation through a series of images. Can be tracked. These difference images can also be processed to emphasize only important information for analysis (defect propagation). However, for diagnostic purposes, the information is 512 × 512 pixels per image and 8 bits per pixel, which is overkill. The only information needed for diagnosis is to follow defect propagation through the series of images.

If the image is processed correctly and the subtraction is well done,
It is possible to start the actual DFI diagnosis. The key to the nature of the defect, its location and time of occurrence can be found somewhere in the stack of difference images. In order to find these keys efficiently, it is important that the images can be accessed quickly and interactively (in a few tenths of a second), displayed and compared visually. One way to do this is to display all the images in the stack side-by-side and simultaneously to allow easy viewing of defect propagation. However, if each image has 512 x 512 pixels, then only four images can be displayed on a conventional high resolution computer workstation display screen at a time.

One way to display multiple images simultaneously on the screen (to facilitate visual tracking of defect propagation) is to reduce the size of each image into an "icon".
Or compress the image and display it on the screen. For example, if a 512 × 512 pixel image is compressed into a 64 × 64 pixel icon, each pixel of the icon represents a 8 × 8 pixel square portion of the first image. With such an icon, it is possible to display dozens of images simultaneously on the display screen.
However, if you compress the image into an icon, you will lose information (in the example above, you may lose 63/64 information from the first image). High resolution compression of the image is required as the details of the icon are needed for DFI analysis. However, if many icon images are displayed at once, efficient DFI analysis requires that image compression be performed quickly when the image to be displayed is selected from the stack. In order to achieve an "interactive" action, it is desirable to perform any selected process, for example when preparing an icon from an image, and display the result within a period that does not exceed, for example, 2 seconds. .

Systems using convolution to perform geometric operations, filter operations and pattern recognition are known in the art. Such systems may use the Fast Fourier Transform to speed up the computation of large convolutions. Floating point operations are often used because it is not known in advance how many operations will be performed on the data. However, when using floating point arithmetic, the intermediate results are often more accurate than necessary, and thus may be time consuming when performing calculations. If this precision is not required, it is a waste of time and resources.

Another way to speed up image processing is to use a dedicated processor configured to perform certain tasks at high speed. However, the cost of such a processor can significantly increase the cost of the test system. Instead, it is preferable to use a general-purpose processor on a standard engineering workstation to perform image processing without losing processing time.

Aim The present invention has been made in view of the above points, and it is possible to solve the above-mentioned drawbacks of the conventional technology and perform dynamic defect image formation (DFI) with an interactive "feel". For high resolution image compression in workstations of the type provided in systems such as the Schlumberger "IDS 5000" which have sufficient speed to perform and do not require dedicated hardware to perform the processing It is an object of the present invention to provide a method and device.
Another object of the invention is to provide a method and apparatus for high resolution compression of images to icons. Yet another object of the present invention is to provide a compression technique that allows multiple icons to be displayed simultaneously as an aid in DFI analysis of integrated circuits. Yet another object of the present invention is the rapid and interactive compression of voltage contrast images in a general purpose workstation associated with an electron beam test probe system without the need for dedicated computing hardware to perform the compression. Is to provide. Yet another object of the present invention is to provide a technique that enables two-dimensional emulation of a workstation display screen for a three-dimensional display of a stack of images known as a state cube.

Structure The present invention is a method for rapidly compressing an image composed of pixels into a high resolution compressed icon image and using such a method for dynamic defect imaging of operational defects in an integrated circuit. Are offered. By displaying multiple such icons side by side on the screen, it is easy to trace defects within the IC device under test, even by an operator with little knowledge of the device's functionality. It is possible.

According to the present invention, an image formed from n × n pixels is represented by p ×
Compress to a p-pixel icon, where n = p · q and q is an integer, then divide the image into p tiles of q × q pixels, and q tiles from each tile. , Where each of the q pixels represents a predetermined orientation in the tile and the average of the selected q pixels is calculated to represent the tile. This is done by generating a single pixel. Therefore, the pixels representing the tiles form an icon of p × p pixels. Each of the q selected pixels preferably uniquely represents a horizontal row of q pixels, a vertical column of q pixels, and a pair of mutually orthogonal diagonals of the pixels of the tile. . Edge enhancement can also be performed to make the resulting icon sharper.

The present invention further provides a method of dynamically imaging operational defects in integrated circuit devices. Prepare a first stack of strobe voltage contrast images, each of which is an IC
It represents the operating state of the device and has a set of pixels. A second stack of strobe voltage contrast images is provided, each of which represents the operating state of the IC device and has a set of pixels. A third stack of n × n pixel images representing the difference between the images of the first and second stacks is by calculating the difference between the pixel values of the images of the first and second stacks. Be prepared. Compress the plurality of images in the third stack into an icon of p × p pixels, where n = p · q and q is an integer, and when performing the compression, each image is divided into q × q pixels. P tiles and selecting q pixels from each tile, where each of the q selected pixels represents a predetermined orientation in the tile and the q selected pixels are selected. This is done by calculating the average value of the pixels to generate one pixel representing the tile, whereupon the pixels representing the tile form one icon of pxp pixels. It is possible to display a plurality of such icons simultaneously and thus to easily observe the difference in operating conditions between the first stack and the second stack.

Image compression is preferably performed using a suitably programmed general purpose processor associated with the electron beam test probe system.

Thus, the method and apparatus of the present invention allows for rapid and efficient analysis of dynamic processes such as operational defects in integrated circuit devices.

Examples Hereinafter, specific embodiments of the present invention will be described in detail with reference to the accompanying drawings.

An electron beam test probe system 10 useful in analyzing integrated circuits is shown schematically in FIG. 1 in a block diagram.
This electron beam test probe system has three functional elements, namely the electron beam test probe 12
, A circuit exciter 14 and a data processing system 16 with a display terminal 18. The integrated circuit to be analyzed is located within the electron beam test probe 12 and is thus capable of making potential measurements at various points on the IC. The points to be measured are sent by the data processing system 16 to the electron beam test probe 12 via the bus 22. During circuit analysis, it is applied to the integrated circuit by circuit exciter 14 which is connected by bus 24 to the IC under test. The data processing system 16 can be used to identify the test signal pattern to be used and the timing of the potential measurement relative to the test signal pattern. The electron beam test probe system is controlled by an operator who enters commands via the display terminal 18.

The data processing system 16 is shown in block diagram form in FIG. The data processing system 16 can be roughly divided into two functional groups, namely the computing system 50.
And an electron beam test probe control system 52. Here, only the calculation system 50 will be described. The remainder of this system is described in US Pat. No. 4,706,019. Computing system 50
Is capable of storing, processing and displaying high resolution voltage contrast images of the IC under test. The computer system 50 includes a microprocessor 54 and a RAM memory 5
6 and a data storage module 58, which may include a disk drive. Further, the computer system 50 comprises a display terminal 18 having a display interface 60 for driving a high resolution color display terminal 61 having a resolution of at least 1000 x 1000 pixels, for example. The display terminal 18 further includes a keyboard for entering commands and pointer means (eg, a "mouse") for pointing and identifying points on the display screen. The display terminal 18 may also have its own graphic accelerator 62 to reduce the time required to generate the graphic display. Computer system 50 can further include an interface 64 for communicating with other computer systems via communication bus 66.

FIG. 3 shows a pair of strobe voltage contrast images selected from images of two stacks obtained by the Schlumberger "IDS 5000" electron beam test probe system. Each image is formed from an array of 512 x 512 pixels, each pixel having a digital gray scale (halftone) intensity between 0 and 255. Each stack can consist of up to 100 or more images. It is desirable to display a large number of such images simultaneously for DFI analysis, yet sufficient to display only four at a time on the display screen of a typical engineering workstation. It is desirable that the image has a size.

FIG. 4 shows a screen display of a series of icons prepared from a stack of strobe voltage contrast images in accordance with the present invention. The operation of the device under test can be easily traced for each state.

FIG. 5 shows a screen display of a series of icons prepared from a stack of difference images according to the present invention. One icon of one image from each of the two stacks provided with the difference image icon is shown in the upper right part of FIG. The difference image icons (numbered 1 to 30) in the left part of FIG. 5 show the propagation of defects in the device under test. The completely white icons indicate that there are no defects in their operating state. The black lines in the other difference icons represent defects that propagate through the displayed portion of the device under test. The pattern of propagation shows that the defects repeat themselves in a regular correspondence, and then
It is deduced that the incorrect logic level is periodically corrected, for example by a reset signal.

It is one of the objects of the present invention to perform emulation, now known as the state cube. This state cube is a three-dimensional representation of a stack of images. By taking into account the different strobe window delays in the two-dimensional image, a third dimension of time is given. To this end, the present invention provides for the simultaneous juxtaposition of a series of images while maintaining sufficient resolution to allow tracing the movement of the device. It provides a way to compress images into small enough icons. FIG. 2 shows a screen display of a series of icons prepared and displayed according to the method of the present invention.
With such an icon, it is possible to quickly prepare and display a maximum of 100 images (25 MB information).
For example, it has been found that compression and storage of each image requires only about 0.1 seconds when performed on an appropriately programmed Sun Microsystems 3/160 Workstation Processor.

This state cube is emulated with an icon display. This icon is actually a 1 / 8th scaled down version of the actual image. The icon is generated by a method that allows sub-pixel resolution and thus retains most of the information in a full scale image. This high resolution display can be inspected to find the source of the defect by examining the evolution of the icon from one strobe window to the next.

Referring to FIG. 6, assume that an n × n pixel image is compressed into a p × p pixel icon. In addition, the following equation is defined: n = p · q Note that n, p, qεN (that is, n, p, q is an integer) and each pixel has a given value (for example, 0 and Grayscale values between 256). It is possible to divide an nxn image into a grid of tiles, each tile having qxq pixels. Each of these tiles has a 1 in the icon
Contribute to individual pixels.

Within a tile, all pixels appear to have equal information values. Therefore, the simplest solution is to take the average value of all the pixels of the tile to form a single pixel of the icon.

This approach has major drawbacks. This is because there are many pixels to process (q ^{2 in} each tile) and significant time is required to make the necessary calculations.

The present invention provides a method for high resolution compression of images while significantly reducing the computation time on a general purpose digital computer. Divide the operating time by q. Therefore, generating a 64x64 pixel icon from a 512x512 pixel image using the techniques described above requires about eight times as long as the method of the present invention.

The method of the present invention takes advantage of the usual high directional correlation of pixels in the image.

Because of the use of mechanical analogy, it is possible to think of a solid object as having a high correlation axis as it has an inertial axis. These can be axes of symmetry, for example as in images with features having roughly vertical and / or horizontal orientation. Therefore, the image has a feature orientation of 0,
It may have one or two major directions, which is referred to herein as the gray axis, as two-dimensional solids have a 0, 1 or 2 inertial axis. Pixel values along these axes are highly correlated, so it is not necessary to use all of them when calculating the pixel values that form the icon.

If q is not too large (for example, n = 512, p = 6
4 and q = 8), the gray axis is about 0 °, ± 45 ° or 90 °. The closer the image's gray axis is to these axes, the more accurately the icon then represents the prepared image.

Therefore, the solution is to average the grayscale (halftone) values of a set of q pixels, each of these q pixels being alone in the line and alone in the column and , As shown in FIG. 6, alone on its diagonal (line oriented at ± 45 ° and passing through this pixel). As long as q is greater than 3, it is possible to select such a set of pixels. The values in the look-up table can be used to obtain a normalized value for the average value of q pixels, and an icon can be quickly prepared from the image using a suitably programmed general purpose workstation processor. Is.

Another analogy illustrating the technique used by the method of the present invention relates to the "8 queen" chess problem. That is, as shown in FIG. 7, the eight chess queens are arranged at respective positions on the chess board so that no queen takes the other queen. (The piece as the "queen" in chess is
It is possible to move an unlimited number of grids on the chess board in the horizontal, vertical or diagonal directions. When the eight queens are properly placed, none are within range of another.

Each tile in the image can be mapped as a virtual chess board, with each pixel representing a black or white grid of the chess board. The position of the image pixel to be considered for compression is the "queen" in the 8-queen problem.
Is the position. In this way, the pixel correlation is used.

The preferred method of practicing the invention can be carried out in the following sequence of steps.

(1) Select a 512 × 512 pixel image and the intensity level value of each pixel is represented by an 8-bit value (ie, an integer between 0 and 255). If the image is stored as a file in data store 58, its value is read into the register array for processing. When the image is stored in one of the display frame buffers of image processor 74, its value is mapped into a register array.

(2) Divide the image into 64 × 64 tiles of 8 × 8 pixels.

(3) Each tile is converted into an icon pixel having an intensity level value p by averaging an 8-queen type pixel value t (x, y) in the tile. For example, 8p = t (1,2) + t (2,4) + t (3,7) + t (4,3)
+ T (5,0) + t (6,6) + t (7,1) + t (8,5) In an 8 × 8 array t, only one value per line and per column is taken. The next set of values represents one of many possible sets of pixels that satisfy the 8 queens condition. It is possible to use any of these possible sets.

Value in line 1 column 2 value in line 2 column 4 value in line 3 column 7 value in line 4 column 3 value in line 5 column 0 value in line 6 column 6 value in line 7 column 1 value in line 8 column 5 The values are added and the result is divided by 8 (normalized) to obtain the intensity value p of the pixel representing that tile.

The resulting 64x64 array of pixel data p (x, y)
Defines the icon.

(4) Then, preferably, features of interest, such as the width of a metal line of the device under test, may be represented by a small number of pixels, such as two pixels.
The characteristics of the icon are sharpened by convolution with a standard edge enhancement operator. To do this, each value in the array (representing the intensity level of a pixel of the icon) is averaged with the values of surrounding pixels using a weighted average. For example, assigning a positive weight of 8 to each pixel value to be emphasized and a negative weight of -1 to each value of four surrounding pixels, adding the weighted values, and Divide the result by 4 and normalize the resulting pixel values. This process provides efficient enhancement of the edge-defining features of that icon. Such an emphasis operator is conventionally known.
For example, W. Pratt, “Digital Image Processing (DIGITAL IM
AGE PROCESSING) ", (1978) p. 322.

According to one embodiment of the present invention, Sun Microsystems 3 /
It has been found that it is possible to form a 64x64 pixel icon from 512x512 pixels in less than 0.1 seconds using 160 workstations. Further, when the icons are stored in the data storage means 58 together with the images, a series of 100 icons can be searched and displayed in about 2 seconds, facilitating quick interactive DFI diffraction. It turned out to be possible.

Although specific embodiments of the present invention have been described above in detail, the present invention should not be limited to these specific examples, and various modifications can be made without departing from the technical scope of the present invention. Of course,

[Brief description of drawings]

FIG. 1 is a schematic block diagram showing an electron beam test system, FIG. 2 is a schematic block diagram showing a data processing system used in the electron beam test system shown in FIG. 1, and FIG. Illustration of an electron beam photograph showing a screen display of a strobe voltage contrast image, FIG. 4 is an illustration of an electron beam photograph showing a screen display of a series of icons prepared from a stack of strobe voltage contrast images according to the present invention. 5 and 5 are illustrations of electron beam photographs showing a screen display of a series of icons prepared from different image stacks according to the present invention, and FIG. 6 for forming icons according to the present invention. FIG. 7 is an explanatory view showing the compression of the image of FIG. 7, FIG. Explanatory view showing one possible solution against a. (Description of symbols) 10: Electron beam test probe system 12: Electron beam test probe 14: Circuit exciter 16: Data processing system 18: Display terminal 22, 24: Bus 50: Computer system 52: Electron beam test probe control system 60 : Display interface 62: Graphic accelerator 64: Interface

─────────────────────────────────────────────────── ─── Continuation of the front page (51) Int.Cl. ⁶ Identification code Internal reference number FI Technical display location G06T 7/00 H01L 21/82 H04N 1/415 9070-5C 7/18 B 8122-4M H01L 21 / 82 T (56) Reference JP 60-89169 (JP, A) JP 60-142482 (JP, A)

Claims (5)

[Claims] 1. A method of compressing an image of n × n pixels stored in a storage device into an icon of p × p pixels which can be displayed on a display device, wherein n = p · q and q is An integer, (a) dividing the image into p tiles of q × q pixels, and (b) one pixel in each of a plurality of rows and columns defined by q × q pixels in each tile. Select q pixels from each tile such that (c) calculate an average value of the q pixels from each tile to generate a pixel representing the tile. And the pixels representing the tiles form an icon of p × p pixels that can be displayed on a display device. 2. The claim of claim 1 wherein the selected q pixels are not more than one on each of the diagonals defined by the q × q pixels of the tile. The method is characterized by being distributed as follows. 3. A method according to claim 1 or claim 2 including the step of enhancing the icon by convolving the pixels representing the tile with an edge enhancement operator. 4. A method for dynamic imaging of operational defects in an integrated circuit device comprising: (a) a first stack strobe, each image representing an operational state of the device and having a set of pixels. Providing a voltage contrast image, (b) providing a second stack of strobe voltage contrast images, each pixel representing an operating state of the device and having a set of pixels; (c) the first Calculating a difference between pixel values of the stack image and the second stack image to represent a difference between the first stack image and the second stack image of n × n pixel pixels. (3) prepare images of three stacks, and (d) compress the plurality of images of the third stack into icons of p × p pixels, where n = p · q and q is an integer, and the compression is , (I) Each of the images is divided into q × q pixels. (Ii) selecting q pixels from each tile such that there is one pixel in each of a plurality of rows and columns defined by q × q pixels in each tile, (Iii) calculating an average value of the q pixels from each tile to generate one pixel representing the tile, wherein the pixel representing the tile forms one icon of p × p pixels. (E) It is possible to simultaneously display a plurality of the icons, and at that time, it is possible to easily observe a difference in operating state between the first stack and the second stack. A method comprising steps. 5. A device for compressing an image of n × n pixels stored in a storage device into an icon of p × p pixels which can be displayed on a display device, wherein n = p · q. And q is an integer, (a) means for dividing the image into p tiles of q × q pixels, (b) a plurality of rows and columns defined by q × q pixels of each tile. Selecting q pixels from each tile such that there is one pixel in each, and (c) an average value of the q pixels from each tile to generate one pixel representing the tile. A device for calculating a pixel, the pixel representing the tile forming a p × p pixel icon that can be displayed on a display device.